L'Equipe says PSG chiefs are worried as negotiations with the Italy goalkeeper continue to drag on.
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For the moment, Donnarumma's current deal expires in less than a year's time, meaning he can commit to a pre-contract with any foreign club from January 1 ahead of making a Bosman transfer next summer.
And watching developments closely are Premier League trio Manchester City, Chelsea and Manchester United.
Speaking last week, Donnarumma's agent Enzo Raiola said: "We're discussing it. Such a long negotiation isn't unusual when you're talking about the best goalkeeper in the world.
"We're optimistic; PSG is a great club. Let's let these last few games of the season pass and then we'll try to reach an agreement within a reasonable timeframe."